cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A135073 Primes for which the period of the reciprocal equals (p-1)/14.

This page as a plain text file.
%I A135073 #18 Jun 29 2021 05:51:20
%S A135073 449,1289,3557,4397,4999,5209,6203,6637,7043,8387,10613,11369,13147,
%T A135073 13399,14323,16871,18481,19391,20147,20707,26489,28813,29387,29947,
%U A135073 30241,32831,32999,33587,36107,37591,38053,39719,40559,41231,41609
%N A135073 Primes for which the period of the reciprocal equals (p-1)/14.
%C A135073 Also cyclic numbers of the fourteenth degree (or fourteenth order): the reciprocals of these numbers belong to one of fourteen different cycles. Each cycle has the (number minus 1)/14 digits.
%H A135073 Amiram Eldar, <a href="/A135073/b135073.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..57 from R. J. Mathar, Feb 21 2008)
%H A135073 Makoto Kamada, <a href="http://www36.tok2.com/home/kamada/math/">Factorizations of 11...11 (Repunit)</a>.
%e A135073 1289 has period of reciprocal 92, or (1289/1)/14.
%p A135073 A007732 := proc(n) local nred25 ; nred25 := n ; while nred25 mod 2 = 0 and nred25 > 1 do nred25 := nred25/2 ; od; while nred25 mod 5 = 0 and nred25 > 1 do nred25 := nred25/5 ; od; if nred25 = 1 then 1; else numtheory[order](10,nred25) ; fi ; end: for n from 1 to 22000 do p := ithprime(n) ; if 14*A007732(p) = p-1 then printf("%d,",p) ; fi ; od: # _R. J. Mathar_, Feb 21 2008
%t A135073 Select[Prime[Range[4500]],Length[RealDigits[1/#][[1,1]]]==(#-1)/14&] (* _Harvey P. Dale_, Jun 22 2013 *)
%Y A135073 Cf. A097443, A055628, A056157, A056210, A056211, A056212, A056213, A056214, A056215, A056216, A056217, A098680.
%K A135073 nonn,base
%O A135073 1,1
%A A135073 Julien Peter Benney (jpbenney(AT)gmail.com), Feb 12 2008
%E A135073 Corrected and extended by _R. J. Mathar_, Feb 21 2008